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%I #11 Nov 15 2024 07:00:49
%S 1,1,3,4,7,10,17,23,36,48,73,96,140,182,259,334,463,592,806,1024,1370,
%T 1728,2281,2860,3727,4646,5991,7430,9487,11706,14822,18205,22870,
%U 27966,34890,42492,52670,63896,78743,95178,116659,140516,171380,205750
%N The number of overpartitions of n with restricted odd differences and smallest part both odd and overlined.
%C The number of overpartitions of n such that: (i) the difference between successive parts may be odd only if the larger part is overlined and (ii) the smallest part of the overpartition is both odd and overlined.
%H K. Bringmann, J. Dousse, J. Lovejoy, and K. Mahlburg, <a href="https://doi.org/10.37236/5248">Overpartitions with restricted odd differences</a>, Electron. J. Combin. 22 (2015), no.3, paper 3.17.
%F G.f.: 1 + 3*Sum_{n >= 1} a(n)q^n = Product_{n >= 1} (1-q^(3*n))/((1-q^n)*(1-q^(2*n)) * (1 + 2*Sum_{n >= 1} q^(n(n+1)/2)*(1-q^2)(1-q^4)...(1-q^(2*n-2))*(1-q^n)/((1-q^3)(1-q^6)...(1-q^(3*n))).
%Y Cf. A141094, A260890, A261035.
%K nonn
%O 1,3
%A _Jeremy Lovejoy_, Aug 07 2015